Work

A Harris theorem for enhanced dissipation, and an example of Pierrehumbert*

Year: 2025

Type: article

Abstract: In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium—a phenomenon known as enhanced dissipation. Here we study the situation where the advecting velocity field generates a random dynamical system satisfying certain Harris conditions. If κ denotes the strength of the diffusion, then we show that with probability at least 1 − o ( κ N ) enhanced dissipation occurs on time scales of order | ln ⁡ κ | , a bound which is known to be optimal. Moreover, on long time scales, we show that the rate of convergence to equilibrium is almost surely independent of diffusivity. As a consequence we obtain enhanced dissipation for the randomly shifted alternating shears introduced by Pierrehumbert’94.

Source: Nonlinearity

DOI: 10.1088/1361-6544/adc652

Authors: William Cooperman, Gautam Iyer, Seungjae Son

Institutions: Courant Institute of Mathematical Sciences, New York University, Carnegie Mellon University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: National Science Foundation, Division of Mathematical Sciences